1. Field of the Invention
The present invention is a system and method for measuring the dimensions of a small structure, such as a microelectronic device. More particularly, the present invention is an optical measuring device that uses a polarized light beam, reflected off a very small structure, to measure the dimensions of the structure.
2. Background and Summary
Current microelectronics fabrication processes can produce structures as small as 0.25 microns. Indeed, structures even smaller than 0.25 microns will soon be fabricated commercially. (For the remainder of this description, the term "structure" will be used to mean any type of feature to be measured by the present invention, including grooves, pits, lines, bumps, and other three dimensional objects.)
The quality control inspection required at each step of the fabrication process becomes a problem with structures having such small dimensions. The small size allows many structures to be fabricated on a wafer, meaning that more layers of interconnections must also be fabricated on the wafer. Thus, the method for inspecting such devices must be fast and efficient in order to inspect every wafer on a fabrication line. In addition, the method must not damage the wafer.
Several methods currently exist for measuring such small structures, but these methods suffer from disadvantages that prevent their use or at least make them impractical for inspecting microelectronic wafers on-line. One such method employs a scanning electron microscope to measure the structures. This method is expensive and slow, however, because each wafer must be placed in a vacuum chamber, which must then be evacuated, before the measurement can be performed. Moreover, most electron microscopy techniques require that the wafer be cut so that the wafer's profile can be measured. These techniques, therefore, cannot be used to inspect wafers on-line.
Conventional optical microscope methods also cannot be used for such small structures. Such methods can barely resolve structures of this scale and thus do not provide accurate dimensional data.
Another method for measuring such small structures, which employs an atomic force microscope, is even slower than electron microscopy. This method, moreover, is impractical for structures with high aspect ratios, i.e., structures in which the height or depth is much larger than the smallest dimension. An example of a high aspect ratio structure is a contact hole etched through oxide layers for contacting a circuit device with metallization. Another example of a high aspect ratio structure is a capacitor trench etched into a silicon substrate for DRAM cell fabrication.
Optical diffraction methods have also been used to measure small microelectronic structures. These optical methods measure the scatter of plane waves and assume that the structures form gratings (i.e., periodic structures). This assumption, however, generally does not hold. Further, these methods cannot be used to measure individual or aperiodic structures.
Accordingly, the inventor recognized a need for an optical system and method for measuring small individual or aperiodic structures that is fast, efficient, and inexpensive and that overcomes the disadvantages and drawbacks of the prior art. The present invention provides such a system and method.
An object of the present invention is to provide an optical system and method for measuring a lateral dimension or a vertical dimension of a structure by focusing a polarized beam of light onto the structure and measuring the phase and amplitude of the reflected polarization components, where the lateral dimension is smaller than the wavelength of the light beam.
Another object of the present invention is to provide methods for determining the amplitude and phase of the reflected polarization components of the light beam.
Another object of the present invention is to provide methods for testing the stability and accuracy of the method of calculating the amplitude and phase of the polarization components.
Yet another object of the present invention is to provide an apparatus for detecting the reflected polarized light beam.
The system of the present invention employs a light source to generate a beam of light that is polarized and focused onto a structure to be measured. Preferably, the light beam is approximately monochromatic. The structure is illuminated with both a transverse electric (TE) polarized field and a transverse magnetic (TM) polarized field. The structure has a plurality of lateral dimensions (e.g., length and width) and at least one vertical dimension (e.g., depth or height). These lateral and vertical dimensions will be generally referred to throughout this description as "structural parameters." The term "structural parameter" should also be understood to include the type of material making up the structure, e.g., gold or silver. One of these structural parameters is preferably substantially larger than the wavelength of the incident light beam. Another one of the structural parameters is small enough so that, when the incident light is diffracted off the structure, the amplitude and phase of the diffracted TM and TE are affected differently by the structure. Preferably, the light beam has polarization components substantially parallel (TE) and perpendicular (TM) to the larger structural parameter.
The focused light beam is diffracted off the structure and is detected by a detector. The TM and TE fields are affected differently by the diffraction off the structure. The TE field can be used as a reference to analyze the phase and amplitude changes in the TM field. The relationship between phases and amplitudes of the TE and TM fields is dependent on the structural parameters of the structure. Thus, the parameters of the structure can be determined by examining the amplitude and phase relationship between the reflected TE and TM fields.
The system uses beam splitters, wave plates, and detector elements to measure the reflected light beam. Preferably, the light beam propagates through a polarizer and a beam splitter and is focused onto the structure. The light beam then preferably is reflected off the structure and back through the beam splitter. Alternatively, the light beam can be transmitted through the structure. The in-phase and quadrature components of the TM field, using the TE field as a reference, are then measured. The system may have an in-phase and quadrature leg, so that both components can be measured in parallel. Alternatively, the system may have only one leg for measuring the in-phase and quadrature components, with a time delay being employed to measure the components in series. Preferably, the system includes four separate detector elements, two each for the in-phase and quadrature legs. The TE and TM polarized waves can be "interfered" in both the in-phase and quadrature legs.
Another aspect of the invention involves determining the amplitude and phase of the diffracted electromagnetic far fields for each polarization component. One method for determining the amplitude and phase is by a numerical method, which is preferably embodied in a computer program and includes several steps. First, several variables are determined and entered into the computer. The variables include: the wavelength of the focused light beam, the index of refraction of the incident medium (e.g., air), the index of refraction of the diffracting structure, the numerical aperture of the focusing lens, a description of the shape of the structure, and a choice of the type of polarization (e.g., transverse electric or magnetic field polarization). In addition, a maximum extent is selected for the surface of the structure which confines the numerical calculation to a truncated region. Generally, the truncated region is substantially larger than the wavelength divided by the numerical aperture of the focusing lens. An arbitrary spacing of grid of points along the surface of the structure is selected, and a set of basis functions is selected.
Second, lookup tables may be created. This step increases the speed of the computer program, but is not necessary, as the calculations in the third step can be performed (albeit more slowly) without the lookup tables. One such lookup table may include entries representing the geometry of the structure's surface contour. Another lookup table may include the distances along the surface contour from a reference point to each grid point. A third lookup table may include the abscissas and weights used repeatedly in the numerical integrations performed in the next step.
Third, numerical integrations are performed for surface contours of the structure. Each integration provides the tangential electric and magnetic fields along the structure's surface contour at some point. The integrand includes basis functions (preferably, sinc functions, where sinc(x)=sin.pi.x/.pi.x)) and a Green's function. The Green's function is a function of several of the variables input in the first step, such as the wavelength of the light beam and the indexes of refraction of the incident medium and the refracting medium. The number of sinc functions is preferably equal to the number of grid points.
Fourth, a matrix is constructed. Each matrix element is a numerical line integral along the whole surface contour of the structure. Thus, each matrix element includes a numerical integration of a 2-dimensional Green's function and a sinc function. The rows of the matrix represent the grid point on which the Green's function is centered, and the columns represent the grid point on which the sinc function is centered. The matrix accounts for electromagnetic fields and for the surface contour of the structure.
Fifth, the incident electromagnetic field at each grid point along the structure's surface contour is calculated, in known fashion. These incident field values are due only to the incident light beam at the surface contour and thus do not account for diffracted light. These incident field values become the elements of an incident field vector.
Sixth, the matrix is inverted and multiplied by the incident field vector to obtain the elements comprising a previously unknown vector. The unknown vector (a tangential electromagnetic field vector) accounts for diffraction of the light beam. The elements of the electromagnetic field vector represent the actual tangential electric and magnetic fields that are present along the surface contour.
Finally, the tangential electromagnetic field vector is used to calculate the diffracted electromagnetic far field. Both the amplitude and phase of the electromagnetic far field are a function of angle. It is not necessary to calculate both the electric and magnetic far fields. If either the electric or magnetic far field is calculated, as those skilled in the art will appreciate, the other far field can be derived using Maxwell's equations.
This numerical method provides the scattered electromagnetic far field for one polarization component (e.g., the TE component). The method can be repeated to obtain the scattered far field for the other polarization component. The final step is to calculate the phase difference in the Fourier Transform responses of the TE and TM fields and the corresponding in-phase and quadrature response.
An alternative method for determining the phase and amplitude of the electromagnetic far field involves the use of a sample with structures of known dimensions. Here, a set of reference structures is taken, for which the structural parameters are (preferably) precisely known. This reference structure is then measured using the present invention, and the electromagnetic far field polarization responses for the reference structures are determined. Other structures having at least one unknown structural parameter can then be measured in accordance with this invention, and the electromagnetic far field polarization response for each such structure can be compared to that for the reference structures. The unknown structural parameters can then be determined by comparing the measured response of the unknown parameters with the measured responses of the known reference structures. The unknown structural parameters will be most similar to the dimensions of that known reference structure for which the polarization quadrature measurements are most similar.
The present invention also includes methods for testing the stability and accuracy of the numerical method described above. The preferred method for testing the stability is known as a convergence test. The convergence test involves repeating the method for the same structure with an increasing and/or decreasing number (and thus spacing) of grid points. The truncation size of the structure can also be varied while repeating the method. Preferably, however, the truncated length of the structure is kept relatively short to reduce the total number of grid points and thus the time it takes to perform all the calculations. The numerical program is stable if the numerical solution converges (i.e., if the result does not change significantly when varying the number of grid points). The numerical accuracy can be estimated from the convergence data.
Another method for testing the accuracy of the numerical method uses the Fast Fourier Transform (FFT) of surface currents along the contour. The use of sinc functions for the basis functions of the surface current makes the implicit assumption that the surface current is strictly bandlimited in space. The Fourier Transforms should show a cutoff frequency if the surface currents are in fact bandlimited. The highest frequency bin will correspond to the cutoff frequency of the bandlimited functions, if a calculation is made of the FFT of the surface current coefficients, which estimate the tangential electromagnetic field along the contour. The FFTs of the surface current coefficients are then examined to determine whether they have significant amplitudes in the high frequency bins (e.g., by comparing those amplitudes to some expected amplitude). If so, it can be assumed that there is aliasing (i.e., that grid sampling is not being performed fast enough) and that the grid spacing must be decreased.